Walters had a truly miserable time of it when the Blues visited the Britannia Stadium for Saturday's Barclays Premier League match, heading in two own goals and missing a penalty as the Potters were beaten 4-0.
Begovic has no doubt the forward is strong enough to bounce back from that and would not be surprised to see Walters make an immediate return to form by getting on the scoresheet against Palace, who Stoke are hosting for a third-round replay after drawing 0-0 with them in the original tie on January 5.
"I don't think anybody will worry about Jon Walters," Begovic said.
"His character and personality won't be affected by anything that happens to him.
"It was a couple of unfortunate incidents for him. I take the blame for the second goal because I probably should have come for the ball, but seeing him there I decided not to.
"He is a big enough character to bounce back and I am sure he will probably score a goal on Tuesday."